Bu soru , reddit kullanıcısı taho_teg tarafından oluşturulan bu reddit iş parçacığından kaynaklanır, ancak daha genel bir "bulmaca" ya genişletilir.

Merkezi eksen etrafında bir daireye eşit olarak dağıtılmış şişeler için 24 delikli bir santrifüjünüz var. Şimdi birkaç şişeniz varsa ve santrifüjü başlatmak istiyorsanız, bunların dengeli bir şekilde yerleştirildiğinden emin olmanız gerekir. Dengeleyemeyeceğiniz tek şişe sayısı 1 ve 23'tür. Örneğin, 4'ü açıkça dengeleyebilirsiniz, ancak 3 şişe ile bir 'üçgen' oluşturarak ve diğer ikisini iki zıt siteye yerleştirerek 5'i de dengeleyebilirsiniz.

Hedef

Santrifüjünüzün delik sayısını (dönen eksenin etrafındaki bir daireye eşit olarak dağıtılmış) giriş olarak kabul eden ve santrifüjde dengelenemeyen flakonların bir listesini veren bir program yazmanız gerekir.

Hesaplamayı yapmak zorundasınız ve sadece önceden hesaplanmış çözümleri kodlayamazsınız.

Giriş ve çıkış, programın farklı girişler için çağrılması için program kodunun değiştirilmesine gerek kalmayacak şekilde uygulanmalıdır. Konsol aracılığıyla çağrılabilen bir işlev (veya kendi dilinizde benzer bir yapı) yazmak da kabul edilebilir.

Santrifüjünüzde 6 delik varsa, 2 ve 3 flakonu santrifüj edebileceğinizi, ancak 'üçgenin' ve karşı ikisinin bir noktada üst üste bineceği için 5'i dengeleyemeyeceğinizi de unutmayın. Başka bir örnek n = 15 için 11 flakonu dengeleyemezsiniz, 6 ve 5 flakonu dengeleyebilirsiniz, ancak bu çözümlerin kombinasyonu üst üste binecektir (bu elbette bunu yapmanın imkansız olduğu ölçütü değildir).

Güncelleme

Bazı insanlar verilen örneği anlamadılar, bu yüzden burada bir grafik yaptım. LÜTFEN algoritmanızın nasıl çalıştığına dair kısa bir açıklama ve doğrulama için bazı örnek çıktılar yazın. Lütfen aşağıdaki örnekleri ekleyin:

n = 1, 6, 10, 24, 63, 100 = 10^2, 163 (prime), 40320 = 8!, 65536=2^2^2^2^2, 105953 (prime)

40320 ve 65536'nın büyük listeler üreteceğini unutmayın, belki de sadece bu listelerin uzunluğunu belirtmek iyi bir fikir olacaktır.

Bu listeye eklemek için bazı ilginç numaralar biliyorsanız lütfen bana bildirin! Algoritma en az n = 1'000'000'e kadar çalışmalıdır.

Örnek çıktılar:

Bunlar bazı örnek çıktılar, ancak belki de hatalı çünkü bunları sadece elle hesapladım.

1: 1
2: 1
3: 1,2
4: 1,3
5: 1,2,3,4
6: 1,5
7: 1,2,3,4,5,6
8: 1,3,5,7
9: 1,2,4,5,7,8
10:1,3,7,9
11:1,2,3,4,5,6,7,8,9,10
12:1,11
13:1,2,3,4,5,6,7,8,9,10,11,12
14:1,3,5,9,11,13
15:1,2,4,7,8,11,13,14

İpucu

Eğer bir santrifüj varsa n delikleri ve örneğin denge olamaz 6 şişeleri, ayrıca Blance mümkün olmayacaktır n-6 temelde denge aynı görevdir - şişeleri m boş bir santrifüj üzerinde şişeler veya doldurulmuş santrifüj dengelemek için ellerinden alarak m şişeleri. Listenizde m sayısı varsa nm de eklemeniz gerekir .

Adaçayı - 102 104/115

Neden kaba kuvvet varken sayı teorisini kullanalım?

v=lambda n:[j for j in range(n+1)if all(sum(e^(i*2*I*pi/n)for i in c)for c in Combinations(range(n),j))]

Belirli sayıda flakon için bu, flakonları konumlandırmak için tüm yollardan geçer ve karmaşık aritmetikler kullanarak kütle merkezlerini hesaplar. Bu yolların hiçbiri için kütle merkezi sıfır ise, sayı döndürülür.

Ne yazık ki, bu bazı durumlarda işe yaramaz (10,14), çünkü Sage bazı ifadeleri sıfıra ( bu hatayla ilgili olabilir) basitleştiremez . Bu, programın değil yorumlayıcının bir kusuru olarak görülebilir ve yine de algoritmanın ve programın iyi olduğunu söyleyebilir.

Aşağıdaki 113 karakterlik alternatif, semboller yerine şamandıralara dayanır ve bu sorunlardan muzdarip değildir:

v=lambda n:[j for j in range(n+1)if all(abs(sum(exp(i*2j*pi/n)for i in c))>1e-9for c in Combinations(range(n),j))]

113 karakterlik sürümün test çıktısı ( for n in range(14): print n,v(n)):

0 []
1 [1]
2 [1]
3 [1, 2]
4 [1, 3]
5 [1, 2, 3, 4]
6 [1, 5]
7 [1, 2, 3, 4, 5, 6]
8 [1, 3, 5, 7]
9 [1, 2, 4, 5, 7, 8]
10 [1, 3, 7, 9]
11 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
12 [1, 11]
13 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
14 [1, 3, 5, 9, 11, 13]

Çalışma zamanını daha yüksek beklemek istemedim n.

Bu, aşağıdaki Python çözümünden kaynaklanır. Tam aritmetik ve bazı modülleri ithal etmek zorunda kalmamak oldukça önemli.

Python - 173 154 156

from itertools import*
from cmath import*
v=lambda n:[j for j in range(n+1)if all(abs(sum(exp(i*2j*pi/n)for i in c))>1e-9for c in combinations(range(n),j))]

Bu varyantın test çıkışı ( for n in range(24): print n,v(n)):

0 []
1 [1]
2 [1]
3 [1, 2]
4 [1, 3]
5 [1, 2, 3, 4]
6 [1, 5]
7 [1, 2, 3, 4, 5, 6]
8 [1, 3, 5, 7]
9 [1, 2, 4, 5, 7, 8]
10 [1, 3, 7, 9]
11 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
12 [1, 11]
13 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
14 [1, 3, 5, 9, 11, 13]
15 [1, 2, 4, 7, 8, 11, 13, 14]
16 [1, 3, 5, 7, 9, 11, 13, 15]
17 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
18 [1, 17]
19 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]
20 [1, 3, 17, 19]
21 [1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20]
22 [1, 3, 5, 7, 9, 13, 15, 17, 19, 21]
23 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]
24 [1, 23]

Çalışma zamanını daha yüksek beklemek istemedim n.

Lua - 197

Kaba olmayan bir kuvvet yöntemi olan bir faktörler listesi oluşturur ve bunları dışlar. Ayrıca, kullanılan en büyük faktör doldurulmamış deliklerin miktarından daha az olduğu sürece, bu faktörlerin eklenmesi ile elde edilebilecek sayıları da göz ardı eder. Biri her zaman yazdırılır ve algoritmada kullanılmaz.

i=io.read("*n")f={}print(1)for z=2,i do
x=z
if i%x<1 then
table.insert(f,1,x)end
for q=1,#f do
y=f[q]x=x*math.min(1,z%y)while x>=y and x-1~=y and y<=i-z do x=x-y end
end
if x>0 then print(z)end
end

Örnek çıktı: (bazıları aralık olarak koyulur, böylece karakter sınırını aşmam)

1: 1

6: 1,5

10:1,3,7,9

24:1,23

63:1,2,4,5,8,11,13,17,20,22,23,25,26,29,32,34,38,41,44,47,50,53,58,59,61,62

100:1,3,13,23,33,43,53,63,73,83,93,97,99

163:1-162

40320:1,11,13,17,19,29,31,37,41,43,61,71,73,97,113,121,127,139,157,169,179,181,191,193,209,211,221,223,241,251,253,263,269,271,277,281,289,299,307,313,331,337,347,349,353,361,373,377,379,397,401,403,409,421,431,433,437,439,449,461,467,473,479,481,491,493,499,517,521,523,529,533,541,547,571,577,587,589,593,601,607,613,617,619,631,641,653,659,671,673,683,689,691,697,701,703,709,713,731,733,737,739,751,757,761,769,781,793,811,817,841,851,853,857,859,869,871,877,881,883,907,913,929,937,953,961,971,977,979,989,991,997,1003,1009,1019,1021,1027,1033,1037,1039,1049,1051,1069,1073,1079,1081,1093,1121,1133,1139,1151,1153,1163,1171,1177,1181,1189,1193,1201,1213,1217,1223,1237,1243,1249,1261,1271,1273,1277,1279,1289,1291,1297,1301,1303,1321,1331,1333,1357,1361,1363,1369,1373,1381,1387,1409,1417,1429,1441,1451,1453,1457,1459,1469,1471,1481,1483,1489,1501,1511,1513,1531,1537,1553,1567,1579,1597,1601,1609,1619,1621,1633,1643,1649,1651,1661,1663,1681,1691,1693,1697,1699,1709,1711,1717,1721,1723,1741,1751,1753,1777,1793,1801,1807,1819,1837,1849,1859,1861,1871,1873,1889,1891,1901,1903,1921,1931,1933,1937,1949,1951,1957,1961,1963,1969,1991,1993,2011,2017,2027,2029,2033,2041,2047,2053,2057,2059,2077,2081,2087,2089,2101,2113,2129,2137,2143,2161,2171,2173,2197,2207,2209,2221,2227,2237,2239,2251,2257,2269,2273,2281,2297,2311,2321,2353,2369,2381,2419,2431,2449,2461,2477,2491,2503,2509,2521,2531,2533,2537,2539,2549,2551,2557,2561,2563,2581,2591,2593,2617,2633,2641,2647,2659,2677,2689,2699,2701,2707,2713,2717,2719,2729,2731,2749,2753,2759,2761,2773,2801,2809,2827,2833,2843,2857,2867,2869,2879,2881,2893,2897,2899,2909,2911,2917,2921,2923,2929,2941,2951,2953,2971,2977,2993,3001,3007,3019,3037,3041,3049,3061,3071,3083,3089,3091,3103,3121,3131,3133,3149,3151,3161,3169,3179,3181,3187,3193,3211,3217,3229,3233,3251,3253,3257,3259,3277,3281,3289,3293,3301,3313,3317,3319,3329,3341,3347,3359,3361,3371,3373,3377,3379,3389,3391,3397,3401,3403,3421,3431,3433,3457,3473,3481,3487,3499,3517,3529,3539,3541,3551,3553,3569,3571,3581,3583,3601,3611,3613,3623,3629,3631,3637,3641,3649,3659,3667,3673,3691,3697,3707,3709,3713,3721,3733,3737,3739,3757,3761,3763,3769,3781,3791,3793,3797,3799,3809,3821,3827,3833,3839,3841,3851,3853,3859,3877,3881,3883,3889,3893,3901,3907,3931,3937,3947,3949,3953,3961,3967,3973,3977,3979,3991,4001,4013,4019,4031,4033,4043,4049,4051,4057,4061,4063,4069,4073,4093,4097,4103,4117,4129,4153,4159,4171,4177,4187,4189,4201,4211,4213,4223,4237,4241,4243,4253,4267,4273,4283,4297,4301,4303,4309,4313,4321,4331,4337,4339,4363,4369,4379,4381,4387,4393,4409,4411,4427,4429,4433,4441,4447,4453,4463,4469,4471,4477,4481,4493,4499,4511,4513,4517,4523,4537,4541,4553,4561,4577,4601,4607,4609,4619,4621,4637,4649,4661,4673,4691,4703,4717,4721,4733,4751,4757,4769,4787,4793,4801,4811,4813,4817,4829,4841,4853,4859,4877,4883,4889,4897,4901,4913,4919,4939,4957,4961,4973,4979,4997,5003,5009,5017,5021,5027,5041,5051,5053,5057,5059,5069,5071,5077,5081,5083,5101,5111,5113,5137,5153,5161,5167,5179,5197,5209,5219,5221,5231,5233,5249,5251,5261,5263,5281,5291,5293,5303,5309,5311,5317,5321,5329,5339,5347,5353,5371,5377,5387,5389,5393,5401,5413,5417,5419,5437,5441,5443,5449,5461,5471,5473,5477,5479,5489,5501,5507,5513,5519,5521,5531,5533,5539,5557,5561,5563,5569,5573,5581,5587,5611,5617,5627,5629,5633,5641,5647,5653,5657,5659,5671,5681,5693,5699,5711,5713,5723,5729,5731,5737,5741,5743,5749,5753,5771,5773,5777,5779,5791,5797,5801,5809,5821,5833,5851,5857,5881,5899,5917,5921,5939,5941,5951,5953,5963,5969,5981,5983,6001,6011,6023,6029,6031,6037,6049,6059,6061,6067,6073,6091,6107,6109,6113,6121,6131,6133,6137,6157,6161,6163,6169,6173,6191,6193,6197,6199,6221,6227,6233,6239,6241,6253,6257,6259,6277,6281,6283,6289,6301,6313,6331,6337,6347,6353,6361,6367,6373,6379,6401,6413,6431,6443,6449,6451,6457,6463,6469,6473,6481,6491,6493,6497,6499,6509,6511,6521,6523,6529,6541,6551,6553,6571,6577,6593,6611,6613,6617,6619,6631,6637,6641,6649,6667,6673,6689,6697,6721,6731,6733,6737,6739,6749,6751,6757,6761,6763,6781,6791,6793,6817,6833,6841,6847,6859,6877,6889,6899,6901,6911,6913,6929,6931,6941,6943,6961,6971,6973,6983,6989,6991,6997,7001,7009,7019,7027,7033,7051,7057,7067,7069,7073,7081,7093,7097,7099,7117,7121,7123,7129,7141,7151,7153,7157,7159,7169,7181,7187,7193,7199,7201,7211,7213,7219,7237,7241,7243,7249,7253,7261,7267,7291,7297,7307,7309,7313,7321,7327,7333,7337,7339,7351,7361,7373,7379,7391,7393,7403,7409,7411,7417,7421,7423,7429,7433,7451,7453,7457,7459,7471,7477,7481,7489,7501,7513,7531,7537,7561,7571,7573,7577,7579,7589,7591,7597,7601,7603,7627,7633,7649,7657,7673,7681,7691,7697,7699,7709,7711,7717,7723,7729,7739,7741,7747,7753,7757,7759,7769,7771,7789,7793,7799,7801,7813,7841,7853,7859,7871,7873,7883,7891,7897,7901,7909,7913,7921,7933,7937,7943,7957,7963,7969,7981,7991,7993,7997,7999,8009,8011,8017,8021,8023,8041,8051,8053,8077,8081,8083,8089,8093,8101,8107,8129,8137,8149,8161,8177,8191,8203,8209,8219,8221,8233,8243,8257,8269,8273,8287,8299,8317,8327,8329,8333,8341,8353,8363,8369,8371,8377,8401,8411,8413,8417,8419,8437,8441,8443,8459,8461,8467,8473,8479,8497,8501,8503,8509,8513,8531,8537,8543,8557,8563,8569,8579,8581,8587,8593,8597,8599,8609,8611,8641,8651,8653,8657,8669,8671,8677,8681,8683,8689,8717,8723,8737,8747,8749,8753,8761,8767,8773,8777,8779,8797,8801,8803,8809,8821,8833,8849,8857,8881,8917,8921,8923,8929,8933,8941,8947,8971,8977,8989,8993,9001,9017,9041,9043,9049,9053,9061,9067,9073,9083,9089,9091,9097,9101,9103,9109,9113,9133,9137,9143,9157,9169,9197,9203,9209,9217,9227,9229,9241,9253,9257,9259,9277,9281,9287,9301,9307,9313,9337,9341,9343,9349,9353,9361,9367,9389,9397,9409,9419,9421,9427,9433,9437,9439,9449,9451,9469,9473,9479,9481,9493,9517,9521,9523,9529,9533,9547,9553,9577,9589,9601,9617,9631,9643,9649,9659,9661,9673,9683,9697,9707,9713,9727,9739,9757,9761,9763,9769,9773,9781,9787,9809,9817,9829,9841,9857,9871,9883,9889,9899,9901,9913,9923,9937,9949,9953,9967,9979,9997,10001,10009,10013,10021,10027,10033,10049,10057,10069,10081,10091,10093,10097,10099,10109,10111,10117,10121,10123,10141,10151,10153,10177,10193,10201,10207,10219,10237,10249,10259,10261,10271,10273,10289,10291,10301,10303,10321,10331,10333,10343,10349,10351,10357,10361,10369,10379,10387,10393,10411,10417,10427,10429,10433,10441,10453,10457,10459,10477,10481,10483,10489,10501,10511,10513,10517,10519,10529,10541,10547,10553,10559,10561,10571,10573,10579,10597,10601,10603,10609,10613,10621,10627,10651,10657,10667,10669,10673,10681,10687,10693,10697,10699,10711,10721,10733,10739,10751,10753,10763,10769,10771,10777,10781,10783,10789,10793,10811,10813,10817,10819,10831,10837,10841,10849,10861,10873,10891,10897,10921,10931,10933,10937,10939,10949,10951,10957,10961,10963,10987,10993,11009,11017,11033,11041,11051,11057,11059,11069,11071,11077,11083,11089,11099,11101,11107,11113,11117,11119,11129,11131,11149,11153,11159,11161,11173,11201,11213,11219,11231,11233,11243,11251,11257,11261,11269,11273,11281,11293,11297,11303,11317,11323,11329,11341,11351,11353,11357,11359,11369,11371,11377,11381,11383,11401,11411,11413,11437,11441,11443,11449,11453,11461,11467,11489,11497,11509,11521,11531,11533,11537,11539,11549,11551,11561,11563,11569,11581,11591,11593,11611,11617,11633,11647,11659,11677,11681,11689,11699,11701,11713,11723,11729,11731,11741,11743,11761,11771,11773,11777,11779,11789,11791,11797,11801,11803,11821,11831,11833,11857,11873,11881,11887,11899,11917,11929,11939,11941,11951,11953,11969,11971,11981,11983,12001,12011,12013,12017,12029,12031,12037,12041,12043,12049,12071,12073,12091,12097,12107,12109,12113,12121,12127,12133,12137,12139,12157,12161,12167,12169,12181,12193,12209,12217,12223,12241,12251,12253,12277,12287,12289,12301,12307,12317,12319,12331,12337,12349,12353,12361,12377,12391,12401,12433,12449,12461,12499,12511,12529,12541,12557,12571,12583,12589,12601,12611,12613,12617,12619,12629,12631,12637,12641,12643,12661,12671,12673,12697,12713,12721,12727,12739,12757,12769,12779,12781,12787,12793,12797,12799,12809,12811,12829,12833,12839,12841,12853,12881,12889,12907,12913,12923,12937,12947,12949,12959,12961,12973,12977,12979,12989,12991,12997,13001,13003,13009,13021,13031,13033,13051,13057,13073,13081,13087,13099,13117,13121,13129,13141,13151,13163,13169,13171,13183,13201,13211,13213,13229,13231,13241,13249,13259,13261,13267,13273,13291,13297,13309,13313,13331,13333,13337,13339,13357,13361,13369,13373,13381,13393,13397,13399,13409,13421,13427,13439,13441,13451,13453,13457,13459,13469,13471,13477,13481,13483,13501,13511,13513,13537,13553,13561,13567,13579,13597,13609,13619,13621,13631,13633,13649,13651,13661,13663,13681,13691,13693,13703,13709,13711,13717,13721,13729,13739,13747,13753,13771,13777,13787,13789,13793,13801,13813,13817,13819,13837,13841,13843,13849,13861,13871,13873,13877,13879,13889,13901,13907,13913,13919,13921,13931,13933,13939,13957,13961,13963,13969,13973,13981,13987,14011,14017,14027,14029,14033,14041,14047,14053,14057,14059,14071,14081,14093,14099,14111,14113,14123,14129,14131,14137,14141,14143,14149,14153,14171,14173,14177,14179,14191,14197,14201,14209,14221,14233,14251,14257,14281,14291,14293,14297,14299,14309,14311,14317,14321,14323,14347,14353,14369,14377,14393,14401,14411,14417,14419,14429,14431,14437,14443,14449,14459,14461,14467,14473,14477,14479,14489,14491,14509,14513,14519,14521,14533,14561,14573,14579,14591,14593,14603,14611,14617,14621,14629,14633,14641,14653,14657,14663,14677,14683,14689,14701,14711,14713,14717,14719,14729,14731,14737,14741,14743,14761,14771,14773,14797,14801,14803,14809,14813,14821,14827,14849,14857,14869,14881,14891,14893,14897,14899,14909,14911,14921,14923,14929,14941,14951,14953,14971,14977,14993,15007,15019,15037,15041,15049,15059,15061,15073,15083,15089,15091,15101,15103,15121,15131,15133,15137,15139,15149,15151,15157,15161,15163,15181,15191,15193,15217,15233,15241,15247,15259,15277,15289,15299,15301,15311,15313,15329,15331,15341,15343,15361,15371,15373,15377,15389,15391,15397,15401,15403,15409,15431,15433,15451,15457,15467,15469,15473,15481,15487,15493,15497,15499,15517,15521,15527,15529,15541,15553,15569,15577,15583,15601,15611,15613,15637,15647,15649,15661,15667,15677,15679,15691,15697,15709,15713,15721,15737,15751,15761,15793,15809,15821,15859,15871,15889,15901,15917,15931,15943,15949,15961,15971,15973,15977,15979,15989,15991,15997,16001,16003,16021,16031,16033,16057,16073,16081,16087,16099,16117,16129,16139,16141,16147,16153,16157,16159,16169,16171,16189,16193,16199,16201,16213,16241,16249,16267,16273,16283,16297,16307,16309,16319,16321,16333,16337,16339,16349,16351,16357,16361,16363,16369,16381,16391,16393,16411,16417,16433,16441,16447,16459,16477,16481,16489,16501,16511,16523,16529,16531,16543,16561,16571,16573,16589,16591,16601,16609,16619,16621,16627,16633,16651,16657,16669,16673,16691,16693,16697,16699,16717,16721,16729,16733,16741,16753,16757,16759,16769,16781,16787,16799,16801,16811,16813,16817,16819,16829,16831,16837,16841,16843,16861,16871,16873,16897,16913,16921,16927,16939,16957,16969,16979,16981,16991,16993,17009,17011,17021,17023,17041,17051,17053,17063,17069,17071,17077,17081,17089,17099,17107,17113,17131,17137,17147,17149,17153,17161,17173,17177,17179,17197,17201,17203,17209,17221,17231,17233,17237,17239,17249,17261,17267,17273,17279,17281,17291,17293,17299,17317,17321,17323,17329,17333,17341,17347,17371,17377,17387,17389,17393,17401,17407,17413,17417,17419,17431,17441,17453,17459,17471,17473,17483,17489,17491,17497,17501,17503,17509,17513,17533,17537,17543,17557,17569,17593,17599,17611,17617,17627,17629,17641,17651,17653,17663,17677,17681,17683,17693,17707,17713,17723,17737,17741,17743,17749,17753,17761,17771,17777,17779,17803,17809,17819,17821,17827,17833,17849,17851,17867,17869,17873,17881,17887,17893,17903,17909,17911,17917,17921,17933,17939,17951,17953,17957,17963,17977,17981,17993,18001,18017,18041,18047,18049,18059,18061,18077,18089,18101,18113,18131,18143,18157,18161,18173,18191,18197,18209,18227,18233,18241,18251,18253,18257,18269,18281,18293,18299,18317,18323,18329,18337,18341,18353,18359,18379,18397,18401,18413,18419,18437,18443,18449,18457,18461,18467,18481,18491,18493,18497,18499,18509,18511,18517,18521,18523,18541,18551,18553,18577,18593,18601,18607,18619,18637,18649,18659,18661,18671,18673,18689,18691,18701,18703,18721,18731,18733,18743,18749,18751,18757,18761,18769,18779,18787,18793,18811,18817,18827,18829,18833,18841,18853,18857,18859,18877,18881,18883,18889,18901,18911,18913,18917,18919,18929,18941,18947,18953,18959,18961,18971,18973,18979,18997,19001,19003,19009,19013,19021,19027,19051,19057,19067,19069,19073,19081,19087,19093,19097,19099,19111,19121,19133,19139,19151,19153,19163,19169,19171,19177,19181,19183,19189,19193,19211,19213,19217,19219,19231,19237,19241,19249,19261,19273,19291,19297,19321,19339,19357,19361,19379,19381,19391,19393,19403,19409,19421,19423,19441,19451,19463,19469,19471,19477,19489,19499,19501,19507,19513,19531,19547,19549,19553,19561,19571,19573,19577,19597,19601,19603,19609,19613,19631,19633,19637,19639,19661,19667,19673,19679,19681,19693,19697,19699,19717,19721,19723,19729,19741,19753,19771,19777,19787,19793,19801,19807,19813,19819,19841,19853,19871,19883,19889,19891,19897,19903,19909,19913,19921,19931,19933,19937,19939,19949,19951,19961,19963,19969,19981,19991,19993,20011,20017,20033,20051,20053,20057,20059,20071,20077,20081,20089,20107,20113,20129,20137,20161,20171,20173,20177,20179,20189,20191,20197,20201,20203,20221,20231,20233,20257,20273,20281,20287,20299,20317,20329,20339,20341,20351,20353,20369,20371,20381,20383,20401,20411,20413,20423,20429,20431,20437,20441,20449,20459,20467,20473,20491,20497,20507,20509,20513,20521,20533,20537,20539,20557,20561,20563,20569,20581,20591,20593,20597,20599,20609,20621,20627,20633,20639,20641,20651,20653,20659,20677,20681,20683,20689,20693,20701,20707,20731,20737,20747,20749,20753,20761,20767,20773,20777,20779,20791,20801,20813,20819,20831,20833,20843,20849,20851,20857,20861,20863,20869,20873,20891,20893,20897,20899,20911,20917,20921,20929,20941,20953,20971,20977,21001,21011,21013,21017,21019,21029,21031,21037,21041,21043,21067,21073,21089,21097,21113,21121,21131,21137,21139,21149,21151,21157,21163,21169,21179,21181,21187,21193,21197,21199,21209,21211,21229,21233,21239,21241,21253,21281,21293,21299,21311,21313,21323,21331,21337,21341,21349,21353,21361,21373,21377,21383,21397,21403,21409,21421,21431,21433,21437,21439,21449,21451,21457,21461,21463,21481,21491,21493,21517,21521,21523,21529,21533,21541,21547,21569,21577,21589,21601,21617,21631,21643,21649,21659,21661,21673,21683,21697,21709,21713,21727,21739,21757,21767,21769,21773,21781,21793,21803,21809,21811,21817,21841,21851,21853,21857,21859,21877,21881,21883,21899,21901,21907,21913,21919,21937,21941,21943,21949,21953,21971,21977,21983,21997,22003,22009,22019,22021,22027,22033,22037,22039,22049,22051,22081,22091,22093,22097,22109,22111,22117,22121,22123,22129,22157,22163,22177,22187,22189,22193,22201,22207,22213,22217,22219,22237,22241,22243,22249,22261,22273,22289,22297,22321,22357,22361,22363,22369,22373,22381,22387,22411,22417,22429,22433,22441,22457,22481,22483,22489,22493,22501,22507,22513,22523,22529,22531,22537,22541,22543,22549,22553,22573,22577,22583,22597,22609,22637,22643,22649,22657,22667,22669,22681,22693,22697,22699,22717,22721,22727,22741,22747,22753,22777,22781,22783,22789,22793,22801,22807,22829,22837,22849,22859,22861,22867,22873,22877,22879,22889,22891,22909,22913,22919,22921,22933,22957,22961,22963,22969,22973,22987,22993,23017,23029,23041,23057,23071,23083,23089,23099,23101,23113,23123,23137,23147,23153,23167,23179,23197,23201,23203,23209,23213,23221,23227,23249,23257,23269,23281,23297,23311,23323,23329,23339,23341,23353,23363,23377,23389,23393,23407,23419,23437,23441,23449,23453,23461,23467,23473,23489,23497,23509,23521,23531,23533,23537,23539,23549,23551,23557,23561,23563,23581,23591,23593,23617,23633,23641,23647,23659,23677,23689,23699,23701,23711,23713,23729,23731,23741,23743,23761,23771,23773,23783,23789,23791,23797,23801,23809,23819,23827,23833,23851,23857,23867,23869,23873,23881,23893,23897,23899,23917,23921,23923,23929,23941,23951,23953,23957,23959,23969,23981,23987,23993,23999,24001,24011,24013,24019,24037,24041,24043,24049,24053,24061,24067,24091,24097,24107,24109,24113,24121,24127,24133,24137,24139,24151,24161,24173,24179,24191,24193,24203,24209,24211,24217,24221,24223,24229,24233,24251,24253,24257,24259,24271,24277,24281,24289,24301,24313,24331,24337,24361,24371,24373,24377,24379,24389,24391,24397,24401,24403,24427,24433,24449,24457,24473,24481,24491,24497,24499,24509,24511,24517,24523,24529,24539,24541,24547,24553,24557,24559,24569,24571,24589,24593,24599,24601,24613,24641,24653,24659,24671,24673,24683,24691,24697,24701,24709,24713,24721,24733,24737,24743,24757,24763,24769,24781,24791,24793,24797,24799,24809,24811,24817,24821,24823,24841,24851,24853,24877,24881,24883,24889,24893,24901,24907,24929,24937,24949,24961,24971,24973,24977,24979,24989,24991,25001,25003,25009,25021,25031,25033,25051,25057,25073,25087,25099,25117,25121,25129,25139,25141,25153,25163,25169,25171,25181,25183,25201,25211,25213,25217,25219,25229,25231,25237,25241,25243,25261,25271,25273,25297,25313,25321,25327,25339,25357,25369,25379,25381,25391,25393,25409,25411,25421,25423,25441,25451,25453,25457,25469,25471,25477,25481,25483,25489,25511,25513,25531,25537,25547,25549,25553,25561,25567,25573,25577,25579,25597,25601,25607,25609,25621,25633,25649,25657,25663,25681,25691,25693,25717,25727,25729,25741,25747,25757,25759,25771,25777,25789,25793,25801,25817,25831,25841,25873,25889,25901,25939,25951,25969,25981,25997,26011,26023,26029,26041,26051,26053,26057,26059,26069,26071,26077,26081,26083,26101,26111,26113,26137,26153,26161,26167,26179,26197,26209,26219,26221,26227,26233,26237,26239,26249,26251,26269,26273,26279,26281,26293,26321,26329,26347,26353,26363,26377,26387,26389,26399,26401,26413,26417,26419,26429,26431,26437,26441,26443,26449,26461,26471,26473,26491,26497,26513,26521,26527,26539,26557,26561,26569,26581,26591,26603,26609,26611,26623,26641,26651,26653,26669,26671,26681,26689,26699,26701,26707,26713,26731,26737,26749,26753,26771,26773,26777,26779,26797,26801,26809,26813,26821,26833,26837,26839,26849,26861,26867,26879,26881,26891,26893,26897,26899,26909,26911,26917,26921,26923,26941,26951,26953,26977,26993,27001,27007,27019,27037,27049,27059,27061,27071,27073,27089,27091,27101,27103,27121,27131,27133,27143,27149,27151,27157,27161,27169,27179,27187,27193,27211,27217,27227,27229,27233,27241,27253,27257,27259,27277,27281,27283,27289,27301,27311,27313,27317,27319,27329,27341,27347,27353,27359,27361,27371,27373,27379,27397,27401,27403,27409,27413,27421,27427,27451,27457,27467,27469,27473,27481,27487,27493,27497,27499,27511,27521,27533,27539,27551,27553,27563,27569,27571,27577,27581,27583,27589,27593,27611,27613,27617,27619,27631,27637,27641,27649,27661,27673,27691,27697,27721,27731,27733,27737,27739,27749,27751,27757,27761,27763,27787,27793,27809,27817,27833,27841,27851,27857,27859,27869,27871,27877,27883,27889,27899,27901,27907,27913,27917,27919,27929,27931,27949,27953,27959,27961,27973,28001,28013,28019,28031,28033,28043,28051,28057,28061,28069,28073,28081,28093,28097,28103,28117,28123,28129,28141,28151,28153,28157,28159,28169,28171,28177,28181,28183,28201,28211,28213,28237,28241,28243,28249,28253,28261,28267,28289,28297,28309,28321,28337,28351,28363,28369,28379,28381,28393,28403,28417,28429,28433,28447,28459,28477,28487,28489,28493,28501,28513,28523,28529,28531,28537,28561,28571,28573,28577,28579,28597,28601,28603,28619,28621,28627,28633,28639,28657,28661,28663,28669,28673,28691,28697,28703,28717,28723,28729,28739,28741,28747,28753,28757,28759,28769,28771,28801,28811,28813,28817,28829,28831,28837,28841,28843,28849,28877,28883,28897,28907,28909,28913,28921,28927,28933,28937,28939,28957,28961,28963,28969,28981,28993,29009,29017,29041,29077,29081,29083,29089,29093,29101,29107,29131,29137,29149,29153,29161,29177,29201,29203,29209,29213,29221,29227,29233,29243,29249,29251,29257,29261,29263,29269,29273,29293,29297,29303,29317,29329,29357,29363,29369,29377,29387,29389,29401,29413,29417,29419,29437,29441,29447,29461,29467,29473,29497,29501,29503,29509,29513,29521,29527,29549,29557,29569,29579,29581,29587,29593,29597,29599,29609,29611,29629,29633,29639,29641,29653,29677,29681,29683,29689,29693,29707,29713,29737,29749,29761,29777,29791,29803,29809,29819,29821,29833,29843,29857,29867,29873,29887,29899,29917,29921,29923,29929,29933,29941,29947,29969,29977,29989,30001,30017,30031,30043,30049,30059,30061,30073,30083,30097,30109,30113,30127,30139,30157,30161,30169,30173,30181,30187,30193,30209,30217,30229,30241,30251,30253,30257,30259,30283,30299,30301,30307,30313,30323,30329,30337,30347,30349,30353,30361,30367,30383,30389,30391,30397,30413,30419,30431,30433,30449,30451,30467,30469,30473,30481,30487,30493,30497,30523,30529,30539,30547,30553,30557,30559,30571,30577,30593,30617,30623,30637,30641,30643,30649,30661,30673,30683,30689,30691,30697,30701,30703,30713,30721,30733,30743,30757,30763,30769,30803,30809,30811,30817,30823,30829,30833,30841,30859,30881,30889,30913,30923,30929,30931,30937,30941,30943,30949,30953,30973,30977,30983,30997,31009,31033,31039,31051,31057,31067,31069,31081,31091,31093,31103,31117,31121,31123,31133,31147,31153,31163,31177,31181,31183,31189,31193,31201,31211,31217,31219,31243,31249,31259,31261,31267,31273,31289,31291,31307,31309,31313,31321,31327,31333,31343,31349,31351,31357,31361,31373,31379,31391,31393,31403,31411,31417,31427,31429,31433,31441,31447,31453,31457,31459,31483,31489,31499,31501,31513,31517,31519,31529,31531,31537,31543,31553,31571,31583,31597,31601,31603,31609,31613,31621,31627,31643,31649,31651,31657,31663,31669,31673,31681,31693,31697,31723,31729,31753,31763,31769,31771,31777,31781,31783,31789,31793,31819,31837,31841,31849,31873,31883,31889,31891,31897,31901,31903,31909,31921,31931,31933,31937,31939,31949,31951,31957,31961,31963,31981,31991,31993,32017,32033,32051,32057,32063,32077,32083,32089,32093,32101,32107,32113,32129,32149,32161,32173,32183,32189,32191,32197,32201,32203,32209,32213,32233,32237,32243,32257,32267,32269,32273,32281,32293,32297,32299,32317,32321,32323,32329,32341,32351,32353,32357,32359,32369,32381,32387,32393,32399,32401,32411,32413,32419,32437,32441,32443,32449,32453,32461,32467,32491,32497,32507,32509,32513,32521,32527,32533,32537,32539,32551,32561,32573,32579,32591,32593,32603,32609,32611,32617,32621,32623,32629,32633,32651,32653,32657,32659,32671,32677,32681,32689,32701,32713,32731,32737,32761,32779,32797,32801,32819,32821,32831,32833,32843,32849,32861,32863,32881,32891,32903,32909,32911,32917,32929,32939,32941,32947,32953,32971,32987,32989,32993,33001,33011,33013,33017,33037,33041,33043,33049,33053,33071,33073,33077,33079,33101,33107,33113,33119,33121,33133,33137,33139,33157,33161,33163,33169,33181,33193,33211,33217,33227,33233,33241,33247,33253,33259,33281,33293,33311,33323,33329,33331,33337,33343,33349,33353,33361,33371,33373,33377,33379,33389,33391,33401,33403,33409,33421,33431,33433,33451,33457,33473,33491,33493,33497,33499,33511,33517,33521,33529,33547,33553,33569,33577,33601,33611,33613,33617,33629,33641,33653,33659,33683,33689,33697,33701,33713,33739,33757,33773,33779,33797,33809,33821,33827,33833,33841,33851,33853,33857,33869,33871,33877,33881,33883,33889,33911,33913,33931,33937,33953,33961,33967,33979,33997,34001,34009,34019,34021,34031,34033,34043,34049,34051,34061,34063,34081,34091,34093,34103,34109,34117,34121,34129,34141,34147,34171,34177,34187,34189,34193,34201,34211,34213,34217,34219,34241,34243,34249,34253,34261,34271,34273,34277,34289,34301,34313,34319,34331,34333,34337,34339,34357,34361,34369,34373,34381,34387,34393,34411,34417,34427,34429,34441,34453,34457,34459,34471,34481,34493,34499,34511,34513,34523,34529,34537,34541,34543,34549,34553,34561,34571,34577,34579,34603,34609,34619,34621,34627,34633,34649,34651,34667,34669,34673,34681,34687,34693,34703,34709,34711,34717,34721,34733,34739,34751,34753,34757,34763,34777,34781,34793,34801,34817,34841,34847,34849,34859,34861,34877,34889,34901,34913,34931,34943,34957,34961,34973,34991,34997,35009,35027,35033,35041,35051,35053,35057,35069,35081,35093,35099,35117,35123,35129,35137,35141,35153,35159,35179,35197,35201,35213,35219,35237,35243,35249,35257,35261,35267,35281,35291,35293,35297,35309,35321,35327,35333,35339,35351,35377,35389,35393,35411,35417,35423,35429,35449,35453,35473,35477,35489,35513,35519,35521,35531,35533,35537,35549,35561,35573,35597,35603,35617,35627,35629,35633,35657,35663,35669,35681,35699,35713,35723,35729,35741,35747,35753,35771,35789,35801,35807,35809,35813,35831,35837,35851,35857,35867,35869,35879,35881,35887,35893,35897,35921,35923,35929,35947,35953,35963,35969,35971,35977,35989,35993,36011,36013,36017,36019,36031,36037,36047,36049,36053,36061,36077,36083,36089,36097,36107,36109,36121,36131,36133,36137,36139,36149,36151,36157,36161,36163,36187,36193,36203,36209,36217,36221,36223,36229,36233,36241,36247,36257,36269,36287,36289,36299,36301,36307,36313,36317,36319,36329,36331,36349,36353,36359,36361,36373,36401,36409,36427,36433,36443,36457,36467,36469,36479,36481,36493,36497,36499,36509,36511,36517,36521,36523,36529,36541,36551,36553,36571,36577,36593,36601,36607,36619,36637,36641,36649,36661,36671,36683,36689,36691,36703,36721,36731,36733,36749,36751,36761,36769,36779,36781,36787,36793,36811,36817,36829,36833,36851,36853,36857,36859,36877,36881,36889,36893,36901,36913,36917,36919,36929,36941,36947,36959,36961,36979,36991,37003,37021,37063,37069,37081,37091,37097,37099,37109,37111,37117,37123,37129,37141,37151,37153,37171,37193,37201,37207,37237,37241,37249,37259,37267,37273,37277,37279,37291,37297,37309,37313,37319,37321,37333,37339,37361,37369,37393,37403,37409,37417,37427,37439,37447,37453,37477,37481,37483,37489,37493,37501,37507,37529,37537,37549,37561,37577,37591,37603,37609,37619,37621,37633,37649,37661,37699,37711,37729,37741,37757,37771,37783,37789,37801,37817,37831,37841,37867,37873,37889,37897,37913,37921,37927,37937,37969,37997,38011,38047,38077,38081,38089,38107,38113,38123,38137,38147,38149,38159,38161,38173,38177,38179,38189,38191,38203,38209,38219,38221,38233,38237,38239,38249,38251,38257,38273,38279,38281,38293,38299,38317,38321,38329,38341,38351,38363,38369,38371,38383,38401,38411,38413,38417,38419,38429,38431,38441,38443,38449,38461,38471,38473,38491,38497,38513,38527,38539,38557,38561,38569,38579,38581,38593,38603,38609,38611,38621,38623,38641,38653,38657,38663,38677,38683,38701,38711,38713,38719,38729,38737,38741,38743,38749,38761,38771,38797,38803,38809,38813,38821,38827,38833,38849,38869,38881,38893,38903,38909,38911,38917,38921,38923,38929,38933,38953,38957,38963,38977,38981,38989,38993,39001,39013,39017,39023,39037,39043,39049,39061,39073,39089,39097,39121,39149,39161,39167,39169,39173,39211,39217,39229,39233,39241,39257,39281,39283,39289,39293,39301,39307,39313,39329,39337,39353,39379,39397,39401,39409,39433,39451,39457,39481,39493,39497,39499,39511,39521,39533,39539,39551,39553,39563,39569,39577,39581,39583,39589,39593,39601,39607,39617,39629,39647,39649,39653,39659,39671,39691,39701,39703,39709,39713,39721,39761,39773,39779,39791,39793,39803,39811,39821,39827,39833,39839,39841,39857,39863,39869,39877,39881,39883,39889,39901,39913,39923,39929,39931,39937,39947,39953,39961,39979,40003,40007,40009,40013,40021,40037,40051,40057,40067,40081,40093,40109,40127,40129,40139,40141,40157,40171,40219,40241,40247,40253,40267,40273,40277,40289,40297,40301,40307,40319

65536: This makes my answer go over the character limit (32768 numbers)

105953: 1-105952

Pyth - 39 37 bayt

@ Wrzlprmft'in python cevabının doğrudan çevirisi.

f.Am>.asm^.n1c*.jZyk.nZQd^10_9.cUQTSQ

Açıklama ve muhtemelen daha fazla golf yakında.

Burada çevrimiçi deneyin .